Optimization problems in the design of a structure typically involve finding a set of variables which maximize a chosen objective function. Given an optimization problem requiring an expensive simulation, surrogate models are often constructed to model the response of an objective function to changes in the magnitude of the variables. Therefore fewer evaluations of the expensive simulation are required. Traditional surrogate modelling techniques are not typically employed on problems with more than 15-20 variables due to the adverse effect of problem dimensionality given a small available number of simulations. Variable reduction techniques, such as those of:                Welch, W. J., Buck, R. J., Sacks, J., and Wynn, H. P., “Screening, Predicting and Computer Experiments”. Technometrics, Vol. 34, No. 1, 1992, pp. 15-25; and        Morris, M. D., “Factorial Sampling Plans for Preliminary Computational Experiments”. Technometrics, Vol. 33, No. 2, 1991, pp. 161-174attempt to reduce the number of variables in a problem and therefore make it easier to find an optimum. Such techniques can require a significant fraction of the overall budget set aside for an optimization and offer no guarantee that a number of the original variables will be identified as being significantly important. The performance of these existing techniques can therefore be extremely problem dependant and can result in a poor reduced set of variables if all of the variables have broadly the same impact on a problem. As these traditional variable reduction techniques are restricted to the original variables, the reduced set can also result in a significant reduction of geometric flexibility.        
An optimisation methodology using proper orthogonal decomposition to reduce the design space is described in Kamali, M., Ponnambalam, K., and Soulis, E. D., Integration of Surrogate Optimization and PCA for Calibration of Hydrologic Models, A WATCLASS Case Study, in IEEE International Conference on Systems, Man and Cybernetics. 2007, IEEE: Montreal, QC, Canada. p. 2733-2737. However, the process of Kamali et al. is not suitable for designing a physical structure such as an airfoil section.